Кашурников В.А., Маймистов А.И. Современные проблемы физики твердого тела. Часть1 - Целый и дробный квантовые эффекты Холла
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ɋɈȼɊȿɆȿɇɇɕȿ ɉɊɈȻɅȿɆɕ ɎɂɁɂɄɂ ɌȼȿɊȾɈȽɈ ɌȿɅȺ
_________________________________________________________________________________________________________________________________________________________________________________________________
ɨɬ ɮɚɤɬɨɪɚ ɡɚɩɨɥɧɟɧɢɹ
P
ɦɨɠɟɬ ɫɥɭɠɢɬɶ ɤɪɢɬɟɪɢɟɦ ɞɥɹ ɩɟ-
ɪɟɯɨɞɚ «ɠɢɞɤɨɫɬɶ-ɬɜɟɪɞɨɟ ɬɟɥɨ».
Ɍɚɤ, ɩɪɟɞɫɬɚɜɢɦ ɧɚ ɪɢɫ. 4.2 ɤɨɪɪɟɥɹɰɢɨɧɧɭɸ ɮɭɧɤɰɢɸ
g(
T
), ɪɚɫɫɱɢɬɚɧɧɭɸ ɞɥɹ ɤɪɢɬɢɱɟɫɤɨɝɨ ɡɧɚɱɟɧɢɹ ɮɚɤɬɨɪɚ ɡɚ-
ɩɨɥɧɟɧɢɹ
P
M
, ɞɥɹ ɤɨɬɨɪɨɝɨ ɦɨɦɟɧɬ M
G
ɪɟɡɤɨ ɦɟɧɹɟɬɫɹ. ɉɪɢ
ɢɡɦɟɧɟɧɢɢ ɦɨɦɟɧɬɚ M
G
= 45o51o57 ɜ ɩɚɪɧɨɣ ɤɨɪɪɟɥɹ-
ɰɢɨɧɧɨɣ ɮɭɧɤɰɢɢ ɫɤɚɱɤɨɨɛɪɚɡɧɨ ɭɜɟɥɢɱɢɜɚɸɬɫɹ ɚɦɩɥɢɬɭɞɵ
ɨɫɰɢɥɥɹɰɢɣ. ɗɬɨ ɫɜɢɞɟɬɟɥɶɫɬɜɭɟɬ ɨɛ ɭɫɬɚɧɨɜɥɟɧɢɢ ɜ ɫɢɫɬɟ-
ɦɟ ɛɨɥɟɟ ɫɬɪɨɝɨɝɨ ɭɩɨɪɹɞɨɱɟɧɢɹ, ɩɪɢɫɭɳɟɝɨ ɬɜɟɪɞɨɦɭ ɬɟɥɭ,
ɯɨɬɹ ɮɚɤɬɨɪ ɡɚɩɨɥɧɟɧɢɹ ɟɳɟ ɫɥɢɲɤɨɦ ɛɨɥɶɲɨɣ ɞɥɹ ɨɠɢ-
ɞɚɟɦɨɝɨ WC ɫɨɫɬɨɹɧɢɹ ɜ ɦɚɤɪɨɫɤɨɩɢɱɟɫɤɨɣ ɫɢɫɬɟɦɟ.
Ɋɢɫ. 4.2.
61
ɄȼȺɇɌɈȼɕȿ ɗɎɎȿɄɌɕ ɏɈɅɅȺ
_________________________________________________________________________________________________________________________________________________________________________________________________
ɉɚɪɧɚɹ ɤɨɪɪɟɥɹɰɢɨɧɧɚɹ ɮɭɧɤɰɢɹ g(
T
) ɞɥɹ ɨɫɧɨɜɧɨɝɨ ɫɨɫɬɨɹɧɢɹ ɜ
ɬɨɱɤɚɯ ɪɟɡɤɨɝɨ ɢɡɦɟɧɟɧɢɹ ɨɫɰɢɥɥɹɰɢɣ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɢɡɦɟ-
ɧɟɧɢɹɦ ɭɝɥɨɜɨɝɨ ɦɨɦɟɧɬɚ 51 o57, 57 o63, 63 o69, 69 o75.
ɇɚ ɪɢɫ. 4.3 ɦɵ ɩɨɤɚɡɵɜɚɟɦ ɨɬɧɨɫɢɬɟɥɶɧɭɸ ɚɦɩɥɢɬɭɞɭ ɨɫ-
ɰɢɥɥɹɰɢɣ ɩɨɫɥɟɞɧɟɝɨ (ɬɪɟɬɶɟɝɨ) ɩɢɤɚ ɤɚɤ ɮɭɧɤɰɢɸ ɮɚɤɬɨɪɚ
ɡɚɩɨɥɧɟɧɢɹ ɞɥɹ ɨɫɧɨɜɧɨɝɨ ɫɨɫɬɨɹɧɢɹ. ȼɢɞɧɨ, ɱɬɨ ɜ ɞɢɚɩɚɡɨ-
ɧɟ 0.294 < < 0.34 ɨɫɰɢɥɥɹɰɢɢ ɩɨɞɚɜɥɟɧɵ, ɱɬɨ ɫɜɢɞɟɬɟɥɶ-
ɫɬɜɭɟɬ ɨɛ ɠɢɞɤɨɫɬɢ Ʌɚɮɥɢɧɚ, ɚ ɜɧɟ ɷɬɨɝɨ ɞɢɚɩɚɡɨɧɚ ɪɟɚɥɢ-
ɡɭɟɬɫɹ ɤɪɢɫɬɚɥɥ ȼɢɝɧɟɪɚ.
P
Ɉɬɦɟɬɢɦ ɬɚɤɠɟ ɫɥɟɞɭɸɳɢɟ ɜɚɠɧɵɟ ɮɚɤɬɵ. ɇɟɬ ɫɨɦɧɟ-
ɧɢɹ ɜ ɬɨɦ, ɱɬɨ ɬɨɱɧɨ ɩɪɢ
P
= 1/3 ɨɫɧɨɜɧɨɟ ɫɨɫɬɨɹɧɢɟ (GS)
ɯɨɪɨɲɨ ɨɩɢɫɵɜɚɟɬɫɹ LL, ɩɨɷɬɨɦɭ ɫɥɟɞɭɟɬ ɨɠɢɞɚɬɶ, ɱɬɨ ɭɝ-
ɥɨɜɨɣ ɦɨɦɟɧɬ GS ɛɭɞɟɬ ɪɚɜɟɧ M
G
(a(
P
=1/3))=N
e
(N
e
-1)/
P
=
63. Ɂɚɪɚɧɟɟ ɷɬɨɬ ɮɚɤɬ ɜ ɱɢɫɥɟɧɧɭɸ ɩɪɨɰɟɞɭɪɭ ɧɟ ɛɵɥ ɡɚɥɨ-
ɠɟɧ. Ɋɟɡɭɥɶɬɚɬɵ ɩɨɞɬɜɟɪɞɢɥɢ, ɱɬɨ ɭɝɥɨɜɨɣ ɦɨɦɟɧɬ ɨɫɧɨɜɧɨ-
ɝɨ ɫɨɫɬɨɹɧɢɹ ɞɟɣɫɬɜɢɬɟɥɶɧɨ ɪɚɜɟɧ 63, Ȼɨɥɟɟ ɬɨɝɨ, ɨɛɧɚɪɭ-
ɠɢɥɨɫɶ, ɱɬɨ M
G
= 5N
e
(N
e
-1) = 105 ɩɪɢ ɡɚɩɨɥɧɟɧɢɢ
P
= 0.198
(~1/5),
0.24 0.28 0.32 0.36
0.0
0.1
0.2
0.3
0.4
0.5
P
Ɋɢɫ. 4.3.
Ɉɬɧɨɫɢɬɟɥɶɧɚɹ ɚɦɩɥɢɬɭɞɚ
ɨɫɰɢɥɥɹɰɢɣ ɩɚɪɧɨɣ ɤɨɪɪɟ-
ɥɹɰɢɨɧɧɨɣ ɮɭɧɤɰɢɢ
ɤɚɤ ɢ ɞɨɥɠɧɨ ɛɵɬɶ ɜ ɫɨɫɬɨɹɧɢɢ Ʌɚɮɥɢɧɚ. Ɍɚɤɠɟ ɨɬɦɟɬɢɦ,
ɱɬɨ ɪɚɡɭɦɧɨɫɬɶ “ɫɪɟɞɧɟɩɨɥɟɜɨɣ” ɩɪɨɰɟɞɭɪɵ ɤɨɧɬɪɨɥɹ ɩɥɨɬ-
ɧɨɫɬɢ ɩɨɞɬɜɟɪɠɞɚɟɬɫɹ ɬɟɦ, ɱɬɨ ɩɪɢ
P
< 1/2 ɩɨɥɨɠɟɧɢɟ ɦɚɤ-
62
ɋɈȼɊȿɆȿɇɇɕȿ ɉɊɈȻɅȿɆɕ ɎɂɁɂɄɂ ɌȼȿɊȾɈȽɈ ɌȿɅȺ
_________________________________________________________________________________________________________________________________________________________________________________________________
ɫɢɦɭɦɚ ɩɥɨɬɧɨɫɬɢ ɱɚɫɬɢɰ
U
(R) ɫɨɜɩɚɞɚɟɬ ɫ ɪɚɫɫɬɨɹɧɢɟɦ ɞɨ
ɩɟɪɜɨɣ ɤɨɨɪɞɢɧɚɰɢɨɧɧɨɣ ɫɮɟɪɵ a(
P
). ɉɨɷɬɨɦɭ ɧɟɬ ɫɨɦɧɟ-
ɧɢɹ ɜ ɚɞɟɤɜɚɬɧɨɫɬɢ ɩɨɞɯɨɞɚ ɫ ɮɢɡɢɱɟɫɤɨɣ ɬɨɱɤɢ ɡɪɟɧɢɹ.
Ɉɤɨɧɱɚɬɟɥɶɧɨɟ ɪɟɡɸɦɟ: ɪɟɡɭɥɶɬɚɬɵ ɪɚɫɱɟɬɨɜ ɩɨɞɞɟɪ-
ɠɢɜɚɸɬ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɟ ɞɚɧɧɵɟ ɢ ɫɜɢɞɟɬɟɥɶɫɬɜɭɸɬ ɨ
ɜɨɡɦɨɠɧɨɫɬɢ ɜɢɝɧɟɪɨɜɫɤɨɣ ɤɪɢɫɬɚɥɥɢɡɚɰɢɢ ɜɛɥɢɡɢ ɮɚɤɬɨ-
ɪɨɜ ɡɚɩɨɥɧɟɧɢɹ
P
=1/3, 1/5. Ⱥ ɬɨɱɧɟɟ, ɩɪɨɞɟɦɨɧɫɬɪɢɪɨɜɚɧɨ,
ɱɬɨ ɜɢɝɧɟɪɨɜɫɤɢɣ ɤɪɢɫɬɚɥɥ ɹɜɥɹɟɬɫɹ ɨɫɧɨɜɧɵɦ ɫɨɫɬɨɹɧɢɟɦ
ɩɪɢ
P
< 0.3, ɤɪɨɦɟ ɞɢɚɩɚɡɨɧɚ 0.294 <
P
< 0.34 (ɜɤɥɸɱɚɹ
P
= 1/3), ɝɞɟ ɥɚɮɥɢɧɨɜɫɤɚɹ ɠɢɞɤɨɫɬɶ ɫɭɳɟɫɬɜɟɧɧɨ ɩɪɢɫɭɬɫɬ-
ɜɭɟɬ ɜ ɫɬɪɭɤɬɭɪɟ ɨɫɧɨɜɧɨɝɨ ɫɨɫɬɨɹɧɢɹ. ȼ ɩɪɢɧɰɢɩɟ, ɧɚ
ɩɪɚɤɬɢɤɟ ɦɨɠɟɬ ɧɚɛɥɸɞɚɬɶɫɹ ɰɟɥɚɹ ɰɟɩɨɱɤɚ ɮɚɡɨɜɵɯ ɩɟɪɟ-
ɯɨɞɨɜ “ɜɢɝɧɟɪɨɜɫɤɢɣ ɤɪɢɫɬɚɥɥ” ”ɥɚɮɥɢɧɨɜɫɤɚɹ ɠɢɞɤɨɫɬɶ”
”ɜɢɝɧɟɪɨɜɫɤɢɣ ɤɪɢɫɬɚɥɥ”... ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɦɚɝɧɢɬɧɨɝɨ
ɩɨɥɹ ɢ ɩɪɨɯɨɠɞɟɧɢɢ ɮɚɤɬɨɪɨɜ ɡɚɩɨɥɧɟɧɢɹ ɱɟɪɟɡ ɡɧɚɱɟɧɢɹ,
ɝɞɟ ɬɨɱɧɨ ɪɟɚɥɢɡɭɸɬɫɹ ɫɬɭɩɟɧɶɤɢ FQHE.
Ɂɚɞɚɱɢ.
Ɂɚɞɚɱɚ 4.1 Ʉɚɤɨɜ ɪɚɡɦɟɪ ɝɢɥɶɛɟɪɬɨɜɚ ɩɪɨɫɬɪɚɧɫɬɜɚ, ɬ.ɟ. ɩɨɥɧɨɟ ɱɢɫɥɨ
ɫɨɫɬɨɹɧɢɣ N ɷɥɟɤɬɪɨɧɨɜ ɧɚ m (0-m) ɨɪɛɢɬɚɥɹɯ?
Ɉɬɜɟɬ
:.
N
m
C
1
Ɂɚɞɚɱɚ 4.2. ɉɨɥɭɱɢɬɶ ɹɜɧɨɟ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɦɚɬɪɢɱɧɨɝɨ ɷɥɟɦɟɧɬɚ ɤɭɥɨ-
ɧɨɜɫɤɨɝɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ, ɜ ɛɚɡɢɫɟ ɜɨɥɧɨɜɵɯ ɮɭɧɤɰɢɣ ɩɟɪɜɨɣ ɡɨɧɵ
Ʌɚɧɞɚɭ.
Ɉɬɜɟɬ:
)
,
,(
!!
)2(
)1(
2
1
21
),min(
0
),min(
0
2/1
4
1
3
2
2
2
4
1
1
1
21
32
2
41
1
31
4321
)!(2
,,,
k
kMI
CC
CCkk
V
mm
mm
mm
k
mm
k
i
i
M
mm
kk
kk
kk
m
mmmm
u
u
u
u
¦¦
³
f
0
]1222[
2
)(
),,(
2
21
21
q
e
kkM
q
qV
dqkkMI
C
S
63
ɄȼȺɇɌɈȼɕȿ ɗɎɎȿɄɌɕ ɏɈɅɅȺ
_________________________________________________________________________________________________________________________________________________________________________________________________
ɝɞɟ M = m
1
+ m
2
- ɫɭɦɦɚɪɧɵɣ ɦɨɦɟɧɬ, C
j
i
= i!/(j!(i-j)!), ɢ V
C
(q)-Ɏɭɪɶɟ-
ɤɨɦɩɨɧɟɧɬɚ ɩɨɬɟɧɰɢɚɥɚ ɞɜɭɯɱɚɫɬɢɱɧɨɝɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ. ȼ ɞɜɭɦɟɪɧɨɣ
ɫɢɬɭɚɰɢɢ ɞɥɹ ɤɭɥɨɧɨɜɫɤɨɝɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ V
C
(q)= 2
S
/q, ɢ ɦɚɬɪɢɱɧɵɟ
ɷɥɟɦɟɧɬɵ ɦɨɠɧɨ ɬɨɱɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ ɪɹɞɚ:
CCCC
m
V
mmmm
mm
k
mm
k
M
kkkk
kkM
kk
i
i
mm
mmmm
3
2
2
2
4
1
1
1
21
32
2
41
1
31
4321
!!
)4(
)!(
2
)1(
]1)(2[
4
1
2/1
,,,
21
),min(
0
),min(
0
12
u
u
¦¦
S
Ɂɚɞɚɱɚ 4.3. Ɋɚɫɫɱɢɬɚɬɶ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟ “ɡɚɦɨɪɨɠɟɧɧɨɣ” ɪɟɲɟɬɤɢ ɫ
ɜɧɭɬɪɟɧɧɢɦɢ ɷɥɟɤɬɪɨɧɚɦɢ, ɡɚɩɪɟɳɚɹ ɩɟɪɟɯɨɞɵ ɫ ɧɟɫɨɯɪɚɧɟɧɢɟɦ ɦɨɦɟɧ-
ɬɨɜ (ɬɨɥɶɤɨ ɞɢɚɝɨɧɚɥɶɧɵɟ ɫɥɚɝɚɟɦɵɟ).
Ɉɬɜɟɬ:
Ⱦɥɹ ɩɨɫɬɪɨɟɧɢɹ “ɫɪɟɞɧɟɩɨɥɟɜɨɝɨ” ɫɬɚɛɢɥɢɡɢɪɭɸɳɟɝɨ ɩɨɬɟɧ-
ɰɢɚɥɚ ɫɥɟɞɭɟɬ ɪɚɫɫɱɢɬɚɬɶ ɞɢɚɝɨɧɚɥɶɧɵɟ ɦɚɬɪɢɱɧɵɟ ɷɥɟɦɟɧɬɵ ɞɥɹ ɨɞɧɨ-
ɝɨ ɷɥɟɤɬɪɨɧɚ, ɧɚɯɨɞɹɳɟɝɨɫɹ ɧɚ ɨɪɛɢɬɟ |m>, ɢ ɞɪɭɝɨɝɨ ɷɥɟɤɬɪɨɧɚ, “ɡɚɦɨ-
ɪɨɠɟɧɧɨɝɨ” ɧɚ ɨɪɛɢɬɟ <
m
=0
(z-Z
j
) . ɉɨɫɥɟ ɪɚɫɱɟɬɚ ɩɨɥɭɱɚɟɦ
m
MF
m
j
j
VV
()
, ...
¦
§
©
¨
·
¹
¸
23
Z
,
ɝɞɟ ɫɭɦɦɚ ɩɨɞɪɚɡɭɦɟɜɚɟɬɫɹ ɩɨ ɜɫɟɦ ɤɨɨɪɞɢɧɚɬɚɦ, ɧɚɱɢɧɚɹ ɫɨ ɜɬɨɪɨɣ
ɤɨɨɪɞɢɧɚɰɢɨɧɧɨɣ ɫɮɟɪɵ, ɢ
>@
m
j
m
m
k
k
k
m
C
mk
q
j
VZ m
kmk
dq
V
q
q
eJ
q
Z
§
©
¨
·
¹
¸
u
f
§
©
¨
·
¹
¸
¦
³
()
!
()
!( )!
()
1
2
1
2
2
2
0
221
0
0
2
S
.
Ɂɞɟɫɶ J
0
(q) - ɮɭɧɤɰɢɹ Ȼɟɫɫɟɥɹ. ɉɨɫɥɟɞɧɟɟ ɜɵɪɚɠɟɧɢɟ ɦɨɠɧɨ ɬɚɤɠɟ
ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ ɪɹɞɚ (ɫɚɦɨɫɬɨɹɬɟɥɶɧɚɹ ɡɚɞɚɱɚ).
Ɂɚɞɚɱɚ 4.4. Ɋɚɫɫɱɢɬɚɬɶ ɩɪɟɞɵɞɭɳɭɸ ɡɚɞɚɱɭ ɜ ɭɫɥɨɜɢɹɯ ɧɟɫɨɯɪɚɧɟɧɢɹ
ɫɭɦɦɚɪɧɨɝɨ ɦɨɦɟɧɬɚ ɢ ɭɱɟɬɨɦ ɩɟɪɟɯɨɞɨɜ ɦɟɠɞɭ ɦɨɦɟɧɬɚɦɢ ɜɧɭɬɪɟɧɧɢɯ
ɷɥɟɤɬɪɨɧɨɜ. ɉɨɤɚɡɚɬɶ, ɱɬɨ ɨɛɳɢɣ ɜɢɞ ɜɵɪɚɠɟɧɢɹ ɛɭɞɟɬ
¦
21
2121
)()(
mm
mm
MF
mm
MF
aaVV
ɢ ɪɟɚɥɢɡɨɜɵɜɚɬɶɫɹ ɛɭɞɭɬ ɩɟɪɟɯɨɞɵ ɫ ɢɡɦɟɧɟɧɢɟɦ ɦɨɦɟɧɬɚ ɧɚ 'm =m
1
-
m
2
= r6n , ɝɞɟ n -ɰɟɥɨɟ.
64
ɋɈȼɊȿɆȿɇɇɕȿ ɉɊɈȻɅȿɆɕ ɎɂɁɂɄɂ ɌȼȿɊȾɈȽɈ ɌȿɅȺ
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Ɂɚɞɚɱɚ 4.5. ɉɨɥɭɱɢɬɶ ɩɪɟɞɟɥɶɧɵɟ ɡɧɚɱɟɧɢɹ ɞɥɹ ɦɚɬɪɢɱɧɵɯ ɷɥɟɦɟɧɬɨɜ
“ɫɪɟɞɧɟɩɨɥɟɜɨɝɨ” ɩɨɬɟɧɰɢɚɥɚ ɧɚ ɛɨɥɶɲɢɯ ɪɚɫɫɬɨɹɧɢɹɯ:
ɍɤɚɡɚɧɢɟ
: ɫɥɟɞɭɟɬ ɪɚɫɫɦɨɬɪɟɬɶ ɨɛɳɟɟ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɷɧɟɪɝɢɢ ɜɡɚɢ-
ɦɨɞɟɣɫɬɜɢɹ ɞɜɭɯ ɱɚɫɬɢɰ i,j ɧɚ ɛɨɥɶɲɨɦ ɪɚɫɫɬɨɹɧɢɢ:
¦
³
<<
<<
1321
34
12
22**
)()(
1
)()(
mmmm
jij
m
j
m
ji
imimij
rdrdrr
rrR
rrV
&&
&
ɢ ɪɚɡɥɨɠɢɬɶ ɟɝɨ ɩɪɢ ɛɨɥɶɲɢɯ R
ij
.
Ɂɚɞɚɱɚ 4.6. ɉɨɥɭɱɢɬɶ ɹɜɧɵɣ ɜɢɞ ɜɨɥɧɨɜɨɣ ɮɭɧɤɰɢɢ ɢɞɟɚɥɶɧɨɝɨ ɜɢɝɧɟ-
ɪɨɜɫɤɨɝɨ ɤɪɢɫɬɚɥɥɚ ɞɥɹ 7-ɦɢ ɷɥɟɤɬɪɨɧɨɜ ɧɚ 31 ɨɪɛɢɬɟ, ɪɚɡɥɨɠɟɧɧɨɣ ɩɨ
ɨɞɧɨɱɚɫɬɢɱɧɨɦɭ ɛɚɡɢɫɭ |m>.
Ɂɚɞɚɱɚ 4.7. Ʉɚɤ ɦɨɠɧɨ ɩɨɫɬɪɨɢɬɶ ɜɨɥɧɨɜɭɸ ɮɭɧɤɰɢɸ ɥɚɮɥɢɧɨɜɫɤɨɝɨ
ɫɨɫɬɨɹɧɢɹ (1.3.6) ɜ ɛɚɡɢɫɟ |m>, ɞɥɹ ɫɟɦɢ ɷɥɟɤɬɪɨɧɨɜ ɧɚ 31 ɨɪɛɢɬɟ (ɭɤɚ-
ɡɚɬɶ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɭɸ ɩɪɨɰɟɞɭɪɭ ɞɥɹ ɱɢɫɥɟɧɧɨɝɨ ɩɨɫɬɪɨɟɧɢɹ) ?
Ɂɚɞɚɱɚ 4.8. ɉɨɥɭɱɢɬɶ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɨɣ ɩɥɨɬɧɨɫɬɢ
( ɫɟɦɢ ɷɥɟɤɬɪɨɧɨɜ ɧɚ 31 ɨɪɛɢɬɟ ɱɟɪɟɡ ɨɩɟɪɚɬɨɪɵ ɪɨɠɞɟɧɢɹ
ɢ ɭɧɢɱɬɨɠɟɧɢɹ ɧɚ ɨɪɛɢɬɚɥɹɯ |m> ɢ ɨɞɧɨɱɚɫɬɢɱɧɵɟ ɜɨɥɧɨɜɵɟ
ɮɭɧɤɰɢɢ ɜ ɩɟɪɜɨɣ ɡɨɧɟ Ʌɚɧɞɚɭ.
)|),(|
2
yx<
mm
aa ,
Ɂɚɞɚɱɚ 4.9. ȼɵɪɚɡɢɬɶ ɩɚɪɧɭɸ ɤɨɪɪɟɥɹɰɢɨɧɧɭɸ ɮɭɧɤɰɢɸ (1.4.4)
g
D
(
T
) = <
D
|<
+
(z
1
)<
+
(z
2
)<(z
2
)<(z
1
)|
D
>, |z
1
|= |z
2
| = a ,
ɹɜɧɨ ɱɟɪɟɡ ɨɩɟɪɚɬɨɪɵ ɪɨɠɞɟɧɢɹ ɢ ɭɧɢɱɬɨɠɟɧɢɹ ɜ ɛɚɡɢɫɟ |m>.
mm
aa ,
________________________________
__________________
65
ɄȼȺɇɌɈȼɕȿ ɗɎɎȿɄɌɕ ɏɈɅɅȺ
_________________________________________________________________________________________________________________________________________________________________________________________________
ɅɂɌȿɊȺɌɍɊȺ
Ɉɫɧɨɜɧɚɹ
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1979.ɬ.1. 399 ɫ. ɬ.2. 422 ɫ.
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